PSI - Issue 24

Francesco Castellani et al. / Procedia Structural Integrity 24 (2019) 495–509 F. Castellani et al. / Structural Integrity Procedia 00 (2019) 000–000

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Furthermore, some additional mechanical properties of blades have to be added in FAST input files. This software, under a mechanical point of view, consider the blades as cantilevered beams: for this reason both these components have to be discretized in a finite number of sections and, for each, some parameters have to be provided inside the input file. In particular, cross-section area, surface density and moment of inertia have been calculated at di ff erent points of the blade and then inserted in the appropriate input file in a tabular format. Similarly to the blades, the wind turbine tower is modeled in FAST as a cantilevered beam: for this reason it has been necessary to compile an input file with the mechanical properties of a total of 80 discrete sections of the tower. Information about tower has been gathered in Bas et al. (2012), where base and top sections dimensions resulted to be: • tower height: 78.54 m; • material: steel plate; Knowing the geometry of tower top and base sections, diameter and wall thickness have been linearly interpolated to find the dimensions of intermediate sections. To confirm the assumption of linearly variable diameter and thickness from base to top, the total weight of the tower has been calculated and compared with the technical data sheet of the turbine. As the error on the weight is limited (less than 5%), the estimation of middle sections geometry has been considered reliable. As done for blades, for the tower, the areas and moments of inertia have been calculated areas for all the sections and then implemented in FAST through a tabular input file. Once all the aerodynamic and mechanical properties have been defined, in the subsequent step, generator and pitch controllers are implemented. Since FAST o ff ers many alternatives to simulate the controllers, for this study an interface between the software and an external environment has been realized. Whereas it would be possible to manage torque and pitch actuators inside FAST routines, in this peculiar case, where non-standard control strategies have to be tested, it has been preferred to use an additional software with whom FAST can be interfaced. In a wind turbine the generator applies a resistant torque to the high speed shaft producing electric power as output. In order to ensure the optimal power production, the relation between shaft speed and torque has to be defined with accuracy. The wind turbine generator characteristic curve is usually divided in four sections, or area:s • area 1: when the shaft speed is lower than a reference startup speed, the generator is turned o ff and the generator applies no torque; • area 2: above the startup speed, in the second area, with an extension of about 1000 RPM, the dependency of torque with respect the shaft speed is parabolic. In this area, the shaft is accelerated and the electric power is produced: • area 2 + 1 / 2: in this zone the torque is increased linearly respect shaft speed; • area 3: when the shaft reaches the rated speed, the torque is kept constant at its maximum value. Information about speed vs torque curve have been found in Churchfield M.J. (2012): the startup speed results to be 560 RPM and the rated one 1456 RPM; in addition mathematical formulas for area 2 and 2 + 1 / 2 are provided, and resumed in Eq.1 and Eq. 2 T 2 = 0 . 004 HS S V 2 (1) T 21 / 2 = 424 . 3 HS S V − 602039 , (2) where T 2 and T 21 / 2 are the torque values in areas 2 and 2 1 / 2 expressed in Nm, HSSV is the High Speed Shaft Velocity in RPM. Thanks to this relations, it is possible to obtain in each moment the torque that the generator has to apply to the shaft. The produced power is then calculated as product between torque and HSSV, converted in rad / s. Once the torque has been calculated according to the previous equations, the values are provided to a Proportional • base diameter(maximum): 4.2 m; • top diameter(minimum): 2.392 m; • wall thickness: 13-41 mm;